Algebra 2 CP
Name______________________
Date_______________________
13.1 – 13.3 Quiz Review
Find the values of the six trigonometric functions for angle θ.
1.
θ
2.
6
3. 2
5
a
θ
θ
13
8
3
Write an equation involving sin, cos, or tan that can be used to find x, then solve the equation.
If no exact answer can be found, round measures of sides to the nearest tenth.
4.
5.
8
30°
6.
x
5
x
60°
x
10
7.
60°
5
x
22°
Solve ΔABC by using the given measurements. Round measures of sides to the
nearest tenth and measures of angles to the nearest degree.
A
8. A = 72°, c = 10
9. B = 20°, b = 15
c
b
C
10. A = 80°, a = 9
11. A = 58°, b = 12
a
B
Draw an angle with the given measure in standard position.
12. 185°
y
O
15. 495°
x
y
O
y
13. 810°
O
14. 390°
x
y
16. -50°
x
O
x
O
17. -420°
x
y
y
x
O
Rewrite each degree measure in radians and each radian measure in degrees.
18. 130°
19. 720°
20. 210°
21. 90°
22. -30°
23. -270°
24.
27.

25.
3
5
4
5
6
28. 
26.
3
4
2
3
29. 
7
6
Find one angle with positive measure and one angle with negative measure coterminal with
each angle.
30. 45°
31. 60°
32. 370°
33. -90°
34.
5
2
35.

36. 
6
3
4
Find the exact values of the six trigonometric functions of θ if the terminal side of θ in
standard position contains the given point.
37. (5, 12)
38. (3, 4)
39. (8, -15)
40. (-4, 3)
41. (-9, -40)
42. (1, 2)
Sketch each angle. Then find its reference angle.
y
y
43. 135°
44. 200°
O
x
O
45.
x
5 y
3
O
x
Find the exact value of each trigonometric function.
46. sin 150°
47. cos 270°
48. cot 135°
50. tan

4
51. cos
4
3
52. cot (-π)
49. tan (-30°)
 3 
53. sin  

 4 
Suppose θ is an angle in standard position whose terminal side is in the given quadrant. For
each function, find the exact values of the remaining five trigonometric functions of θ.
4
12
54. sin θ = , Quadrant II
55. tan θ =  , Quadrant IV
5
5
56. Find the arc length and the area of the sector with a radius of 10 inches and a central
angle of θ = 100°.
57. A stepladder has an angle of elevation of 60° with the front of the house.
The length of the stepladder is 24 feet. At what height does the stepladder meet the house?
58. A flagpole casts a shadow of 10 feet long. Viewed from the end of the shadow, the top of the
flagpole makes a 63° angle with the ground. Sketch a diagram that represents this situation.
What is the height of the flagpole.
Answers.
4
5
4
tan θ =
3
5
sec θ =
3
3
5
5
csc θ =
4
1. sin θ =
5
13
5
tan θ =
12
13
sec θ =
12
cos θ =
cot θ =
2. sin θ =
3
4
12
13
13
csc θ =
5
12
cot θ =
5
4. tan 30° =
8
x = 8 3 ≈ 13.9
x
5. cos 60° =
7. sin 60° =
x
5 3
x=
≈ 4.3
2
5
8. a ≈ 9.5, b ≈ 3.1, B = 18°
10. b ≈1.6, c ≈ 9.1, B = 10°
12. 185°
13. 810°
x
y
17. -420°
3
2
x
10
cos θ =
x ≈ 4.0
9. a ≈ 41.2, c ≈ 43.9, A = 70°
x
x
18.
15. 495°
13
18
x
O
y
x
O
y
16. -50°
O
6. tan 22° =
14. 390°
O
y
23. 
5
x ≈ 10
x
2 13
13
13
csc θ =
3
2
cot θ =
3
3. sin θ =
11. a ≈ 19.2, c ≈ 22.6, B = 32°
y
O
3 13
13
3
tan θ =
2
13
sec θ =
2
cos θ =
21.
19.
4

y
20.
7
6
22. 
2
x
O

6
24. 60°
25. 150°
26. 120°
27. 225°
28. -135°
29. -210°
30. 405°, -315°
31. 420°, -300°
32. 10°, -350°
33. 270°, -450°
34.
12
5
37. sin θ =
cos θ =
13
13
12
13
csc θ =
5
12
13
5
sec θ =
cot θ =
5
12
tan θ =

2
,
3
2
13 11
,
6
6
4
3
38. sin θ =
cos θ =
5
5
35.
4
csc θ =
3
5
sec θ =
cot θ =
3
tan θ =
5
4
3
4
36.
5 11
,
4
4
39. sin θ = 
15
8
cos θ =
17
17
15
8
17
sec θ =
8
tan θ = 
17
15
8
cot θ = 
15
csc θ = 
3
5
cos θ = 
tan θ = 
5
3
csc θ =
3
4
40. sin θ =
sec θ = 
4
5
tan θ =
5
4
cot θ = 
4
3
csc θ = 
41
40
47. 0
2
2
49. 
48. -1
54. cos θ = 
3
5
tan θ = 
4
3
50
inches;
9
3
3
50. 1
5
4
5
3
cot θ = 
3
4
Area of Sector:
250
inches2
9
5
cot θ =
3
x
O
51. 
1
2
52. undefined
55. sin θ = 
csc θ =
csc θ =
y

x
O
sec θ = 
56. Arc Length:
sec θ =
45.
x
O
1
2
tan θ = 2
41
9
cot θ =
9
40
44. 20°
2 5
5
cos θ =
5
5
42. sin θ =
y
43. 45°
53. 
40
9
sec θ = 
y
46.
40
9
cos θ = 
41
41
41. sin θ = 
5
12
cos θ =
13
13
csc θ = 
sec θ =
57. 20.78 feet
13
12
13
5
cot θ = 
5
12
58. 19.6 feet
5
2
1
2